ICMS

Mathematical challenges and modelling of hydroelasticity

Jun 21, 2010 - Jun 24, 2010

15 South College Street, Edinburgh EH8 9AA

Organisers

Name	Institution
Korobkin, Alexander	University of East Anglia
Parau, Emilian	University of East Anglia
Vanden-Broeck, Jean-Marc	University College London

 

Short report

Hydro-elasticity is concerned with deformations of elastic bodies responding to hydrodynamic excitations which themselves depend on elastic deformations. Problems of hydro-elasticity are coupled, which implies that elastic deformations of the body are dependent on hydrodynamic forces and vice versa. The mathematical theory of hydro-elasticity and mathematical methods of solving complex hydro-elastic problems are not well-developed at present. This is viewed as a major obstacle to adequate and successful treatment of problems of hydro-elasticity both in academic research and applications. The aim of the workshop was to identify and to outline mathematical problems of modern hydroelasticity, to review recent developments in this rapidly advancing field, to specify directions to solving hydroelastic problems and to establish contacts between international leaders and young researchers, which may lead to joint international and national projects on mathematical hydroelasticity. In order to achieve this aim, the invited speakers were from four main areas: Mathematics, Fluid Mechanics, Engineering Science and Industry. Papers in the mathematical theory of hydro-elastic waves, floating elastic plates, very large flexible ships, biomechanics, and marine hydrodynamics were presented. Several young researchers made contacts with leading experts in the field and new collaborations were established.

 Download the full report here.

 

Introduction to workshop

The problems of hydroelasticity are important in biology, medicine, offshore and polar engineering, as well as in many industrial applications. However, the mathematical theories of hydroelasticity and mathematical methods of solving complex hydroelastic problems are not well developed yet. This is viewed as a major obstacle to adequate and successful treatment of problems of hydroelasticity arising in applications.

The aim of this workshop is to identify and to outline mathematical problems of modern hydroelasticity, to review recent developments in this rapidly advancing field, to develop new directions for solving hydroelastic problems and to establish contacts between international leaders and young researchers, which will lead to joint international and national projects on mathematical hydroelasticity. In order to achieve this aim, the invited speakers will be from three main areas: Mathematics, Engineering Science and Industry.

The mathematical theory of hydroelasticity should provide a rigorous basis for modern industrial and engineering projects. These projects are concerned with hydroelastic waves in the presence of ice cover in cold regions, springing and whipping analysis in the design of ultra large ships, dynamic behaviour of deep-water risers, sloshing in liquefied natural gas tanks with flexible insulation system, dynamic behaviour of very large floating structures such as floating airports. These topics and their mathematical modelling will to be covered during this Workshop. Each of these topics represents both an important engineering application and a challenging mathematical problem.

The Workshop at ICMS will allow researchers, who are working in the field of mathematical hydroelasticity, to become more aware of other theoretical developments in this field. This is the first Workshop which is focused on mathematical aspects of hydroelasticity.

Confirmed speakers to date
D. Abrahams (University of Manchester)
M. Blyth (University of East Anglia)
P. Brocklehurst (University of East Anglia)
R. Eatock-Taylor (University of Oxford)
C. Eloy (IRPHE Marseilles)
S. Gavryliuk (Aix-Marseille University)
O. T, Gudmestad (University of Stavanger)
M. Haragus (University of Bescancon)
S.E. Hirdaris (Lloyd's Register, London)
R.J. Hosking (Brunei Darussalam University )
G. Iooss (University of Nice)
H. Kalish (University of Bergen)
G.K. Kapsenberg (MARIN)
T.I. Khabakhpasheva (Lavrentyev Institute of Hydrodynamics)
V. Kubenko (University of Kiev)
S. Malenica (Bureau Veritas, Paris)
A. Metrikine (University of Delft)
M. Meylan (University of Auckland)
T. Miloh (Tel Aviv University)
J. Oliver (University of Oxford)
J. Ockendon (OCIAM, Oxford)
N. Peake (University of Cambridge)
P. Plotnikov (Lavrentyev Institute of Hydrodynamics)
R. Schulkes (Statoil)
F. Smith (UCL)
V. Squire (University of Otago)
M. Tucsnak (University of Nancy)

Arrangements

Participation
Participation is by invitation only. People interested to participate should contact the organisers. The workshop will begin on Monday 21 June and finish on Thursday 24 June 2010.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.

Venue
The workshop will be held at 15 South College Street, Edinburgh. All lectures will be held in the Newhaven Lecture Theatre. To view this room and a list of the visual equipment available click here. In addition, two blackboards have recently been installed. Follow this link for a map showing the location of 15 South College Street, or this map may also prove useful.

Wireless Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival you will be given instructions and a code for accessing the wireless network.

Registration
Registration will take place on the morning of Monday 21 June 2010.

Talks
Presentations should be in the formats .pdf or .ppt and should be brought on a memory stick to the workshop, or can be e-mailed to Helene Frossling in advance. 

Travel
Information about travel to the UK and Edinburgh is available here. 

The airport bus costs 3.50 GBP for a single and 6.00 GBP for an open return journey. A taxi directly from the airport will cost approximately 15.00 to 20.00 GBP to the city centre for a one-way journey.

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 22-26 George Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk. The second railway station is called Haymarket and is at the West End of the city centre.

In the light of recent travel disruptions across Europe due to the Icelandic volcano eruption: IF YOU EXPERIENCE ANY DELAYS TO YOUR TRAVEL TO EDINBURGH THAT WILL AFFECT WHICH DAY YOU ARRIVE, PLEASE ADVICE HELENE FROSSLING BY E-MAIL A.S.A.P. 

 

Programme

 

Monday 21 June

09.00 - 09.40	Registration and coffee/tea
09.40 - 09.45	Welcome & Health and Safety information
09.45 - 10.30	Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics) view presentation Strain-gradient theory of hydroelastic travelling waves
10.30 - 11.00	Geert K. Kapsenberg (MARIN) view presentation Slamming of ships: where are we now?
11.00 - 11.30	Henrik Kalisch (University of Bergen) Stability of a CO2-seawater interface
11.30 - 12.00	Sergey Gavrilyuk (University Aix-Marseille) view presentation Solid-fluid diffuse interface model
12.00 - 12.30	Discussion: Moderator John Toland
12.30 - 14.00	Lunch
14.00 - 14.30	Mariana Haragus (Université de Franche-Comté) Transverse spectral stability of travelling periodic waves for the KP equations
14.30 - 15.00	Michael Meylan (University of Auckland) view presentation Hydroelasticity from the perspective of complex scattering frequencies
15.00 - 15.30	Coffee break
15.30 - 16.00	Tatiana Khabakhpasheva (Lavrentyev Institute of Hydrodynamics) view presentation Mathematical aspects of water wave interaction with floating elastic plate
16.00 - 16.30	Rodney Eatock Taylor (University of Oxford) view presentation Resonances and transient responses of a floating beam
16.30 - 17.30	Discussion: Moderator V. Squire
17.30 - 18.30	Wine reception

 

Tuesday 22 June

09.00 - 10.00	Vernon Squire (University of Otago) view presentation Hydroelastic chronicles of a gelid Mathematician
10.00 - 10.30	Roger Hosking (University of Adelaide)-- this talk will be streamed live from New Zealand view presentation(pdf) (ppt) Theoretical response of floating plates to moving loads
10.30 - 11.00	Coffee/tea
11.00 - 11.30	Ruben Schulkes (Statoil) Some fluid-structure interaction problems in the energy industry
11.30 - 12.00	Eldad Avital (Queen Mary University of London) view presentation Sound scattering and control by free surface piercing and fluid loaded cylindrical shells
12.00 - 12.30	Discussion: Moderator John Ockendon
12.30 - 14.00	Lunch
14.00 - 14.30	Luke Bennetts (University of Otago) view presentation Numerical and experimental modelling of synthetic "sea ice" in a wavetank
14.30 - 15.00	Gérard Iooss (IUF, Université de Nice) Nonlinear reduction method for finding localized travelling waves in a fluid layer covered by an elastic plate
15.00 - 15.30	Coffee break
15.30 - 16.00	Jean-Marc Vanden-Broeck (University College London) view presentation Nonlinear waves under a sheet of ice.
16.00 - 16.30	Emilian I. Parau (University of East Anglia) view presentation Three-dimensional solitary waves in fluid mechanics
16.30 - 17.00	Discussion: Moderator R. Eatock Taylor
19.00	Informal dinner at The Magnum restaurant, 1 Albany Street

Wednesday 23 June

09.00 - 09.45	Nigel Peake (University of Cambridge) view presentation Fluid-structure interaction in the presence of mean flow
09.45 - 10.15	Sime Malenica (Bureau Veritas Paris) view presentation Overview of hydroelastic problems in ship design
10.15 - 10.45	Coffee/tea
10.45 - 11.15	Michael Makasyeyev (National Academy of Science of Ukraine) view presentation Two-dimensional unsteady planing elastic plate
11.15 - 11.40	Paul Brocklehurst (University of East Anglia) 3D problem of hydroelastic waves interacting with a vertical column
11.40 - 12.05	Alan Tassin (LBMS - DCNS) view presentation Three-dimensional water impact problems: numerical modelling based on the Wagner theory and experiments
12.05 - 12.30	Discussion: Moderator Richard Purvis
12.30 - 14.00	Lunch
14.00 - 14.30	Frank T. Smith (UCL) view presentation(part 1) (part 2) Many-body problems in fluids
14.30 - 15.00	Mark Blyth(University of East Anglia) Transit of an elastic capsule through a branching channel
15.00 - 15.30	Coffee break
15.30 - 16.00	Christophe Eloy (IRPHE) view presentation Optimisation of undulatory swimming
16.00 - 16.30	Marius Tucsnak (University of Nancy) Mathematical analysis of some swimming mechanisms
16.30 - 17.00	Discussion: Moderator T. Miloh
19.00	Workshop dinner at Blonde Restaurant,  75 St Leonard's St.

Thursday 24 June

09.00 - 09.30	Spyros E. Hirdaris (Lloyd's Register London) view presentation Hydroelasticity of Ships - The classification prespective
09.30 - 10.00	Ove T. Gudmestad (University of Stavanger) view presentation On the concept of negative damping
10.00 - 10.30	Andrei Metrikine (Delft University of Technology) Intermittancy of the self-excited vibrations of a submerged cantilever pipe aspiring water
10.30 - 11.00	Coffee/tea
11.00 - 11.30	Paul A. Martin (Colorado School of Mines) view presentation Multiple scattering of flexural waves by random configurations of inclusions in thin plates
11.30 - 12.00	Malte Peter (University of Augsburg) view presentation The generalised eigenfunction method and time-dependent linear water-wave impact on a vertical elastic plate
12.00- 12.30	Discussion: S. Malenica
12.30 - 13.30	Lunch
13.30 - 14.00	James Oliver (University of Oxford) Second-order Wagner theory for the two-dimensional water entry of a deformable body
14.00 - 14.30	Alexander Korobkin (University of East Anglia) view presentation(pdf) (ppt) Normal mode method in problems of liquid impact onto elastic wall
14.30 - 15.00	Discussion and closing

Presentations:

Presentation Details
Avital, Eldad
Sound Scattering and Control by Free Surface Piercing and Fluid Loaded Cylindrical Shells
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The interaction between a monochromic sound wave and a thin cylindrical shell piercing shallow water surface is considered. The cylindrical shell is clamped to the floor and may be filled with fluid or is empty inside. This model problem is relevant for a variety of applications ranging from off-shore structures to underwater vessels. Linear acoustics and elastic shell dynamics are assumed. Fourier transforms in the vertical and azimuthal directions are used and the shell’s deflection is found by matching its acceleration with the outer and inner fluid pressures. Sound control is achieved by assumed a distribution of pressure actuators acting on the cylindrical wall. Sound field analysis is carried out for an Aluminium shell of 30 cm diameter and 5 meter depth and for low to mid range sound frequencies of 5000 Hz to 20KHz. It is shown that adding fluid inside the cylindrical shell can reduce the scattered sound field level, but does not profoundly change it, still showing reflections in front and sidewise of the shell and a V wake behind it. An equation for a continuous control pressure to cancel the scattered sound is derived and the effect of using a practical configuration of discrete pressure line actuators is shown to have a moderate to a good capability of reducing the scattered sound wave.
Bennetts, Luke
Numerical and experimental modelling of synthetic `sea ice' in a wavetank
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Sea ice floes that form in the polar oceans are modelled as floating thin-elastic plates, as their horizontal dimensions far exceed their thicknesses and as they are known to flex in response to wave forcing. Much theoretical work has been achieved in modelling the interaction of ocean waves with regions of sea ice over the last twenty years, especially under linear and time harmonic assumptions. However, the same period has been devoid of experimental data, which hinders progress. Whilst field work in this area involves long, expensive expeditions in unpredictable conditions, it is hoped that some insight can be gained from wavetank experiments on synthetic floes that will be conducted this year. An outline of these will be presented along with complementary mathematical models.
Blyth, Mark
Transit of an elastic capsule through a branching channel
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The transit of an elastic fluid-filled capsule through a channel with a side branch is investigated numerically using the boundary integral method for Stokes flow. The capsule is carried in a pressure-driven flow of fluid of generally different viscosity to that inside the capsule. Far upstream and downstream in the main channel, and downstream in the side branch, the fluid velocity profiles are assumed to adopt those of unidirectional Poiseuille flow with prescribed flow rates. The capsule boundary is treated as a two-dimensional elastic membrane developing elastic tensions and bending moments. Results are presented for different flow rates through the side branch, for different capsule sizes, and for different side branch angles.
Brocklehurst, Paul
Use of Weber transform and eigenfunction matching to solve hydroelastic wave interaction with a cylinder
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The linear two-dimensional problem of hydroelastic waves diffracting around a vertical mounted cylinder is analysed. The water is of finite depth and covered by an ice sheet. The infinite ice sheet is modelled by linear elastic plate theory and is clamped to the vertical structure. A regular two-dimensional incident wave approaches from infinity and is diffracted by the cylinder. An analytic solution is found by Weber transform. We determine the ice deflection, the vertical and horizontal forces acting on the wall and the principal strains in the ice sheet.
Eatock Taylor, Rodney
Preliminary title "Resonances and transient responses of a floating beam"
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The presentation uses the integral equation for the total hydrodynamic pressure under a floating flexible beam, discretised by a Galerkin approach with Legendre polynomials as the basis functions. The link with classical ship hydroelasticity theory is reviewed, based on the modes of vibration of the "dry" structure. An eigenvalue analysis (c.f. Meylan, IWWWFB 2009) is then performed on the complete coupled hydroelastic equations which result from the Galerkin discretisation. The formulation is used with the FFT to investigate the transient interaction between a flexible beam and an incident focussed wave group (a so-called "NewWave").
Eloy, Christophe
Optimisation of undulatory swimming
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The swimming efficiency of a rigid flapping foil has been addressed by many authors with the aim of modelling the lunate tail of fast swimmers such as sharks, dolphins and tunas. In this case, the problem is governed by few parameters: the heaving and pitching amplitudes and their phase difference. In this talk, we will first review the main results on flapping foils and then consider the general problem of a thin flexible foil undergoing an arbitrary bending motion in two dimensions. Heave and pitch motions will not be prescribed and will arise from force and torque balance on the body. We will show what are the optimal gaits in both the high-speed and low-consumption regimes.
Gavrilyuk, Sergey
Solid-fluid diffuse interface model
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We derive an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov (1978), Miller and Colella (2001), Godunov and Romenski (2003), Plohr and Plohr (2005), Gavrilyuk, Favrie and Saurel (2008). We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.
Gudmestad, Ove T.
On the concept of negative damping
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Damping is limiting the motions of an oscillator, a dynamic system. Different formulations for damping will be discussed. In case the forcing of the dynamic system contains terms proportional to the velocity of motion of the oscillator, the effects will contribute to the damped oscillations. Should the total damping under certain conditions become negative, the oscillations will grow until the damping again has become positive. Investigations on negative damping effects and discussions where negative damping might appear in practical applications will be given.
Haragus, Mariana
Transverse spectral stability of travelling periodic waves for the KP equations
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We discuss the question of spectral stability of one-dimensional periodic travelling waves of the Kadomtsev-Petviashvili equations, KP-I and KP-II, with respect to two-dimensional perturbations. We restrict to periodic waves with small amplitude. Using Floquet decomposition in the direction of propagation, and Fourier decomposition in the perpendicular direction, the spectral stability problem is formulated in terms of the spectra of a two-parameter family of linear operators. These operators have point spectrum, only, and we show how to locate this spectrum, and in particular how to detect instabilities.
Hirdaris, Spyros E.
Hydroelasticity of Ships - The Classification prespective
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The function of Lloyd’s Register includes the setting of standards for the design, construction and maintenance of ship hulls to ensure adequate safety throughout their service life. Fundamental to this is the determination of the design loads. The traditional design philosophy is based on closed form empirical formulae or first principles calculation procedures that, wherever applicable, assume that a ship is a rigid structure. Recently, we have experienced a stepwise increase in ship size and complexity. Examples of this include the whipping and springing response of ULCs and sloshing loads in membrane LNG ships. This raises the need to enhance our understanding on fundamental principles of fluid structure interactions with the aim to provide improved solutions to engineering problems of practical significance. The presentation will outline some of the applications of hydroelasticity theory to ships, with particular reference to recent and ongoing developments focussing on ship design applications and the effects of non-linearities and viscous flows. It will also discuss the longer term potential use of weakly and fully non-linear fluid-structure interaction, as well as Navier Stokes based fluid dynamic methods, for the improved modelling of ship dynamic response problems.
Hosking, Roger
Theoretical Response of Floating Plates to Moving Loads
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In cold regions, relatively smooth floating ice sheets are often exploited by land-based vehicles and as aircraft runways. However, a moving load can produce a much larger deflexion than a stationary load, particularly near a resonance associated with waves it generates in the system. The ice sheet response has been been modelled remarkably successfully by steady state and time-dependent analysis for a justifiably localised load moving over a flexible plate, with both one-dimensional and two-dimensional wave patterns strongly dependent on the load speed. A notable feature in the early theory was the infinite response predicted at one or more critical load speeds. It emerged that the deflexion due to a steadily moving load generally approaches a steady state, but does have a pronounced although finite peak at the critical load speed corresponding to the minimum phase speed (coincident with the group speed) of the flexural-gravity waves generated, when the plate is assumed viscoelastic (anelastic) or nonlinearity is considered. The deflexion due to a line load accelerated through this critical speed was also shown to be bounded. Nevertheless, this load speed should usually be avoided in cold region operations, unless the vehicle happens to be an ice-breaking hovercraft on the St. Lawrence Seaway in Canada for example! The historical theoretical development will be reviewed, together with brief reference to relevant experimental work and also to analogous developments in rail track engineering.
Iooss, Gérard
Nonlinear reduction method for finding localized travelling waves in a fluid layer covered by an elastic plate
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This is a joint work with F. Dias. We consider a perfect fluid layer of finite depth, the flow being potential, and the fluid being covered by an elastic thin plate modeled as a Kirchhoff -Love plate. Using a suitable conformal map, we formulate the problem of the search for traveling waves, as a spatial dynamical system, on which center manifold and normal form reductions methods apply. We study two typical critical situations, the first leading to 1:1 resonance (hamiltonian Hopf bifurcation), the second being a saddle-center bifurcation. The first case may give (this depends on the depth of the fluid layer) localized solitary waves with damping oscillations at infinity, the second case gives generalized solitary waves, with (exponentially) small non damping oscillations at infinity.
Kalisch, Henrik
Stability of a CO2-Seawater Interface
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Wave experiments in a trough filled with liquid CO2 are analyzed. Measurements of regular plane waves excited by a wave maker are used to determine the approximate surface tension of the interface, and the density of the liquid CO2. Thruster experiments are used to investigate the stability of this two-fluid system with respect to currents near the bottom of the ocean. Conditions on the stability of these waves are given, and an approximate damping rate is found.
Kapsenberg, Geert K.
Slamming of ships: where are we now?
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The developments to date will be reviewed and a personal view on what still needs to be done will be presented. The final objective consists of two parts. Part 1 is concerned with the global response of the ship: the impulsive loads need to be predicted, the whipping response can then be calculated and as the final step the associated stresses in the structure. These stresses contribute to the fatigue damage and to the extreme values. Part 2 is concerned with the local stresses due to an impact. These stresses can result in local plastic deformations or damage to stiffeners. Hydroelastic effects are considered to be important for this case. An important aspect is to assess the space and time dependent pressure and to compare this to the “equivalent hydrostatic pressure” as is used in the rules.
Khabakhpasheva, Tatiana
Mathematical aspects of water wave interaction with floating elastic plate
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The investigation of the two-dimensional problem on hydroelastic behavior of a floating plate in periodic surface waves is one of the well prevailing problems of hydroelasticity during the last fifteen years. This problem provides a basic mathematical model for describing the behaviour of very large floating structures such as floating airports. Many results on this topic were obtained numerically and do not involve mathematical substantiation of the exploitable models and methods. As general the hydroelastic problems are coupled and can be subdivided into two or more problems of different types in mathematical sense, each of them separately being well explored (like Neumann problem for Laplace equation or initial problem for Euler beam equation). But coupled problems of hydroelasticity must be investigated and solved simultaneously, which lead to the problem of a totally new type. This indicates a hardship in this type of investigations and explains a small number of analytical results in this field. The present paper deals with mathematical substantiation of the methods of semi-analytical solution of the floating beam problem, proposed by Khabakhpasheva, Korobkin (2002). This method is based on expansion of the hydrodynamic pressure as Fourier series. After substitution of this expansion in the Euler beam equation, with corresponding edge conditions, we have the expansion of the beam deflection with respect to certain basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem (and solve it ones for all) and at the same time to satisfy accurately the beam boundary conditions. Finally the integral equation for the pressure leads to the infinite system of algebraic equations with respect to the principal coordinates. It is shown, that the general matrix of this system is a symmetric matrix, which determines a Hilbert-Schmidt operator. This allows us to apply the method of reduction to solve this problem. It is necessary to emphasize, that in spite of a weak singularity of the pressure at the edges of the plate, elastic parameters of the plate vibration are determined with a good accuracy, because the pressure exerts only a distributed influence on the plate vibrations.
Korobkin, Alexander
Normal mode method in problems of liquid impact onto elastic wall
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Steep wave impact onto elastic wall is studied within both the incompressible liquid model and acoustic approximation. Elastic part of the wall is supported in such a way that the problems can be solved by the method of separating variables. As a result, the contribution of each elastic mode is treated separately. We study convergence of the normal mode series for the hydrodynamic pressure and the stress distribution in the wall. It is shown that the series for the pressure does not converge within the incompressible liquid model if the structural mass of the wall is neglected, and the convergence is rather slow if the structural mass is taken into account. The normal mode series derived for the distribution of the acoustic pressure along the wall well converges and the predicted pressure distributions are reliable.
Makasyeyev, Michael
Two-Dimensional Unsteady Planing Elastic Plate
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The joint hydrodynamics and elasticity two-dimensional problem of planing of elastic plate on the water surface is considered as boundary problem with initial conditions. For the method of fundamental solutions the joint hydroelasticity problem to the one integral equation with the unknown pressure function is reduced. The regimes of steady motion and steady-state oscillation in the issue of limiting process of time to infinity tending are obtained. Because the problem has such unknown values as wetted length, draft and trim angle, it is necessary to add the body dynamics equations to the integral equation of hydroelasticity. For the numerical solution to the integral equations the method of discrete singularities is used. The nonlinear problem of wetted length search is solved with the help of consecutive minimization procedures.
Malenica, Sime
Overview of hydroelastic problems in ship design
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An overview of the selected practical hydroelastic problems which are encountered by the ship structure in her life, are discussed. These problems are related both to the global (springing/whipping) and local (sloshing impacts, slamming,...) hydroelastic issues. Fully non-linear problem being almost impossible to solve, within the present state of the art methods, different simplifications are proposed. The global ship hydroelasticity is solved by coupling the general 3D seakeeping code with the 3DFEM structural model, both in frequency and time domain, using the modal approach. The slamming loading is added using the so called strip approach, because the fully correct 3D slamming model is not available yet. As far as the local hydroelastic problems are concerned, two problems are discussed namely slamming and sloshing impacts. Both are treated using the 2D semi-analytical methods for fluid flow and 3D FE model for structural response. Different impact types are first identified (Wagner, Bagnold, aerated, ...) and for each of them an dedicated semi-analytical fluid flow model is developed and coupled with 3D FE structural model. Finally, the advantages and drawbacks of the pure CFD type of approaches for fluid flow are also discussed.
Martin, Paul A.
Multiple scattering of flexural waves by random configurations of inclusions in thin plates
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Flexural waves are scattered by inclusions or cavities in a thin plate. For a single inclusion, a reciprocity relation (which seems to be new) is obtained connecting coefficients in circular multipole expansions. Then, a formula for the effective wavenumber in a random arrangement of identical inclusions is derived, using the Lax quasi-crystalline approximation. The formula is reminiscent of the Lloyd-Berry formula for acoustic waves, except that it has an additional term and it involves two distinct far-field patterns. This is joint work with William Parnell (University of Manchester).
Metrikine, Andrei
INTERMITTANCY OF THE SELF-EXCITED VIBRATIONS OF A SUBMERGED CANTILEVER PIPE ASPIRATING WATER
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A concept is currently being developed by major offshore companies of liquefying natural gas offshore, on a floating barge. The equipment onboard of such a barge would need a large amount of cooling water, which will be pumped through a set of free-hanging pipes. The industry is interested in the maximum flow rate that could be delivered through the pipes such that they do not become unstable due to the internal flow. Experimental and theoretical investigations have been conducted at TU Delft to answer this question. The experiments showed that a free-hanging submerged pipe aspirating water at a constant speed exhibits what can be called marginal instability and intermittency at the flow velocities higher than a critical. In this talk the experimental findings will be shown and a theory will be presented that explains the intermittent behaviour.
Meylan, Michael
Hydroelasticity from the perspective of complex scattering frequencies
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The basic approach to hydroelasticity is to extend the solution for a rigid body in terms of the six rigid modes of motion, to the case of an infinite number of vibrational modes. While this is a satisfactory method to calculate the response due to an incident wave in the frequency domain, it tells us nothing about the way in which the presence of the fluid effects the vibrational modes. The concept of wet modes goes some way towards achieving this, but requires that some of the fluid effect are neglected. It we want to correctly describe the effect of the fluid on the vibrational modes we require the use of complex scattering frequencies. These are mathematically difficult objects to work with, because they require the solution be found for complex frequencies, which appear unphysical, and which cannot be found using existing commercial software. I will show how these scattering frequencies can be found by a number of methods, including an approximate method based on the solution for real frequencies. I will illustrate their importance in various ways, focusing on simple cannonical hydroelastic problems, but also showing how the method can be extended to more complicated problems, such as the vibrational response of a large container ship.
Oliver, James
Second-order Wagner theory for the two-dimensional water entry of a deformable body
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The two-dimensional impact of a prescribed deformable body of small deadrise angle on a half-space of ideal and incompressible liquid is considered within the framework of Wagner's theory from 1932. Systematic matched-asymptotic methods are used to derive expressions for the second-order corrections to the locations of the high-pressure-jet-root regions and for the composite pressure and force on the body. Several applications are discussed.
Parau, Emilian
Three-dimensional solitary waves in fluid mechanics
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Three-dimensional fully-localised solitary-wave solutions are computed by boundary integral methods for different problems arising in fluid mechanics. In particular results for gravity-capillary waves, interfacial waves and waves under an ice sheet will be presented. Other type of three-dimensional nonlinear flows will be considered.
Peake, Nigel
Fluid-structure interaction in the presence of mean flow
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The unsteady motion of an elastic plate with mean flow under conditions of heavy fluid loading is known to exhibit a range of unusual behavior, including absolute instability and negative energy waves. Here we present recent work, both numerical and asymptotic, on the relation of this infinite-plate behavior to finite systems. We consider two cases; a finite elastic plate in a rigid baffle, and a flag. The resonance of the plate is shown to be very well predicted by suitable application of infinite-plate theory, for both cases in which the infinite plate is either convectively unstable or absolutely unstable. For the flag we show that the dynamics of the free downstream end, and in particular the nature of the wake shed into the fluid, is crucial in determining the energy exchange between the plate and the flow.
Peter, Malte
The generalised eigenfunction method and time-dependent linear water-wave impact on a vertical elastic plate
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The generalised eigenfunction method has recently been suggested as a powerful tool for solving time-dependent linear water-wave scattering problems efficiently. Considering the problem of linear water waves impacting on a vertical elastic plate, which can be viewed as a simple model for wave interaction with elastic tank walls, we present a new elegant way of developing the generalised eigenfunction method and show how it can be used for approximating efficiently the long-time behaviour of the solution in near-resonant situations.
Plotnikov, Pavel
Strain-Gradient Theory of Hydroelastic Travelling Waves
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This is a mathematical study of steady two-dimensional waves which propagate without changing shape on the surface of an infinitely deep fluid that moves under gravity, bounded above by a heavy, frictionless, thin (unshearable) elastic sheet. The sheet stays in contact with the zero streamline of the flow and is deformed by internal elastic forces and couples, and inertial forces and gravity, according to the laws of elasticity. The flow, which is supposed irrotational, is at rest at infinite depth and its velocity is stationary relative to a frame moving with the wave. Therefore the pressure exerted by the fluid at a steady streamline depends on its height and the fluid velocity. We study the balancing of these elastic and hydrodynamic effects to produce a steady hydroelastic wave. To do so, it is supposed that the surface membrane is hyperelastic, with a stored energy function that depends on the stretch, the stretch-gradient, and the curvature of the membrane. The problem is then formulated as one for critical points of a Lagrangian. It is notable that the stored energy for travelling waves may be non-convex in the stretch even when the stored energy of the material at rest is convex. The existence of waves is proved by maximizing the Lagrangian in the presence of strain-gradient effects. An understanding of the limiting process, as the coefficient of the strain-gradient term in the elastic energy tends to zero, is the main purpose of the investigation.
Schulkes, Ruben
Some fluidstructure interaction problems in the energy industry
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Interactions between fluids and flexible structures are of occur in many different areas in the energy industry. In this presentation we look at a number of actual specific fluid-structure interactions problems. The problem of ballooning methanol injection lines is presented in some detail. The dynamic response of these injections lines and typical relaxation time scales are considered. Some challenges related to fluid-structure interactions related to renewable energy are also presented.
Smith, Frank T.
Many-body problems in fluids
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The presentation will be based on three main aspects of nonlinear fluid-body or fluid-bodies interaction and will mostly address the regime of relatively high flow rates. First will be a discussion of various mathematical problems that have arisen in recent times concerned with multi-body interactions in surrounding fluid and the effects of increases in the body count, of different geometries and of different flow rates for example. Second, a particular problem will be described which involves one or many moving rigid bodies whose individual and combined motion affects and is affected by all the surrounding fluid regions. Here the emphasis is on the initial value context and the system stability, the eventual occurrence of clashes between the bodies and the behaviour of the system when the number of bodies is large. The third aspect will be concerned with the implications for one or many moving bodies but of flexible shape(s), within the surrounding fluid. All three have been sparked off by biomedical or industrial modelling interests.
Squire, Vernon
Hydroelastic Chronicles of a Gelid Mathematician
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The field of ocean wave / sea ice interactions and the complementary topic of the hydroelastic analysis of pontoon-type, very large floating structures have seen a massive resurgence of interest in the last two decades, documented in syntheses by Squire et al. (1995) and Squire (2007, 2008). Many physical situations that remained unresolved in the early nineties have now been comprehensively studied by mathematicians and engineers using sophisticated techniques that have allowed accurate models to be created that replicate natural wave phenomena occurring in the polar and subpolar seas. Associated with this has been a greater appreciation of the need to deal with heterogeneity, as the material properties and topography of all types of ice in the ocean, i.e. icebergs and ice islands as well as sea ice, varies spatially and temporally. Unfortunately, although models have become ever more sophisticated, a commensurate evolvement of experimental work, either in the laboratory or in the field, has not kept pace, so the data available for testing theory are still much the same as those reported in 1995. The effect of global climate warming is particularly pertinent, as ocean waves are likely to be more intense, to penetrate further and to carry a more destructive payload in a degraded sea ice lamella. I will chronicle the research, paying particular attention to the most recent developments and to where the next few years may take us. Squire, V.A., Dugan, J.P., Wadhams, P., Rottier, P.J. and Liu, A.K. Of ocean waves and sea ice. Annual Review of Fluid Mechanics 27: 115–168 (1995); Squire, V.A. Of ocean waves and sea-ice revisited. Cold Regions Science & Technology 49(2): 110–133 (2007); Squire, V.A. Synergies between VLFS hydroelasticity and sea-ice research. International Journal of Offshore and Polar Engineering 18(4): 241–253 (2008).
Tassin, Alan
Three-dimensional water impact problems: numerical modelling based on the Wagner theory and experiments.
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Some bulbous bows, also used as sonar domes, are made of fibre reinforced plastic and experience high transient loading during slamming events. It is therefore important to study the dynamic response of the structure to water impacts. A preliminary requirement for that is to accurately predict the transient pressure distribution acting on a complex three-dimensional body during water entry. Although CFD techniques make it possible to accurately describe this phenomenon, shipbuilders still need simple practical and efficient tools for preliminary design or optimization. Several models of water impact based on the Wagner approach have been developed for this purpose but most of them are restricted to the two-dimensional case. As the strip method is inaccurate for non-slender bodies, a numerical method has been developed to solve the three-dimensional Wagner problem. The predictions of slamming loads obtained with the proposed model have been compared to results of CFD models and to experimental data. The proposed method makes it possible to quickly compute the pressure distribution occurring during slamming events and will be used to analyse the dynamic response of bulbous bows to such loads.
Tucsnak, Marius
Mathematical analysis of some swimming mechanisms
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We are interested in the mathematical analysis of self-propelles motions of solids in a fluid (swimming). The high and the low Reynolds regimes are considered, the latter from a control theoretic view point.
Vanden-Broeck, Jean-Marc
Nonlinear waves under a sheet of ice.
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We consider the propagation of nonlinear waves in a layer of water bounded above by a sheet of ice. Weakly nonlinear and fully nonlinear solutions are considered. Periodic waves and solitary waves with decaying oscillatory tails are presented.

Participants

Name	Institution
Abrahams, David	University of Manchester
Avital, Eldad	Queen Mary University of London
Bennetts, Luke	University of Otago
Blyth, Mark	University of East Anglia
Bonnaud, Axel	University of Stavanger
Brocklehurst, Paul	University of East Anglia
Den Besten, Henk	Delft University of Technology
Eatock Taylor, Rodney	University of Oxford
Eloy, Christophe	IRPHE
Gavrilyuk, Sergey	University Aix-Marseille
Gudmestad, Ove T.	University of Stavanger
Haragus, Mariana	Université de Franche-Comté
Hirdaris, Spyros E.	Lloyd's Register London
Hosking, Roger	University of Adelaide
Iooss, Gérard	IUF, Université de Nice
Kalisch, Henrik	University of Bergen
Kapsenberg, Geert K.	MARIN
Khabakhpasheva, Tatiana	Lavrentyev Institute of Hydrodynamics
Korobkin, Alexander	University of East Anglia
Makasyeyev, Michael	Institute of Hydromechanics National Academy of Science of Ukraine
Malenica, Sime	Bureau Veritas Paris
Martin, Paul A.	Colorado School of Mines
Metrikine, Andrei	Delft University of Technology
Meylan, Michael	University of Auckland
Miloh, Touvia	University of Tel Aviv
Oliver, James	University of Oxford
Parau, Emilian	University of East Anglia
Peake, Nigel	University of Cambridge
Peter, Malte	University of Augsburg
Plotnikov, Pavel	Lavrentyev Institute of Hydrodynamics
Reinhard, Moritz	University of East Anglia
Schulkes, Ruben	Statoil
Smith, Frank T.	University College London
Squire, Vernon	University of Otago
Tassin, Alan	University of East Anglia
Toland, John	Isaac Newton Institute for Mathematical Sciences
Tucsnak, Marius	University of Nancy
Vanden-Broeck, Jean-Marc	University College London